Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
import sys
cin = sys.stdin
def solve():
	n,m = map(int,cin.readline().split(' '))
	g = [map(int,cin.readline().split(' ')) for i in xrange(n)]
	check = True
	for i in xrange(n-1):
		ls = [(g[i+1][j]-g[i][j]) for j in xrange(m)]
		if ls!=([ls[0]]*m):
			check=False
	if not check :
		print -1
		return 
	st = g[0][0]
	rows = [g[i][0]-st for i in xrange(n)]
	cols = [g[0][j]-st if j>0 else 0 for j in xrange(m)]
	mrw,mcl = min(rows),min(cols)
	sm = sum(rows)+sum(cols)
	mn = 1000000000000000
	idx=-1
	for i in xrange(501):
		if (i+mrw)>=0 and (st-i)>=0 and ((st-i)+mcl)>=0 :
			vl = ((i*n+(st-i)*m)+sm)
			if vl<mn:
				mn=vl
				idx=i
	rows = [idx+elem for elem in rows]
	cols = [(st-idx)+elem for elem in cols]
	print mn	
	for i in xrange(n) :
		for j in xrange(rows[i]):
			print "row",(i+1)
	for i in xrange(m) :
		for j in xrange(cols[i]):
			print "col",(i+1)
solve()